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A computer-assisted optimal depth lower bound for nine-input sorting networks

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Abstract

It is demonstrated, using a combination of theoretical and experimental computer science, that there is no nine-input sorting network of depth six. If a nine-input sorting network of depth six exists, then there exists one with very special structure. There is an efficient algorithm for constructing and testing comparator networks of this form. This algorithm was implemented and executed on a supercomputer.

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References

  1. M. Ajtai, J. Komlós, and E. Szemerédi. AnO(n logn) sorting network. InProc. 15th Ann. ACM Symp. on Theory of Computing, pages 1–9, April 1983.

  2. M. Ajtai, J. Komlós, and E. Szemerédi. Sorting inc logn parallel steps.Combinatorica, 3:1–48, 1983.

    Google Scholar 

  3. K. E. Batcher. Sorting networks and their applications. InProc. AFIPS Spring Joint Computer Conference, volume 32, pages 307–314, April 1968.

  4. J. R. Bitner, G. Ehrlich, and E. M. Reingold. Efficient generation of the binary reflected gray code and its applicationsComm. ACM, 19(9):517–521, September 1976.

    Google Scholar 

  5. R. C. Bose and R. J. Nelson. A sorting problem.J. Assoc. Comput. Mach., 9:282–296, 1962.

    Google Scholar 

  6. R. W. Floyd and D. E. Knuth. The Bose-Nelson sorting problem. In J. N. Srivastava, editor,A Survey of Combinatorial Theory. North-Holland, Amsterdam, 1973.

    Google Scholar 

  7. D. E. Knuth.The Art of Computer Programming, volume 3. Addison-Wesley, Reading, MA, 1973.

    Google Scholar 

  8. I. Parberry. The alternating sorting network. Technical Report CS-87-26, Department of Computer Science, Penn State University, September 1987.

  9. I. Parberry.Parallel Complexity Theory. Research Notes in Theoretical Computer Science. Pitman, London, 1987.

    Google Scholar 

  10. I. Parberry. A computer-assisted optimal depth lower bound for sorting networks with nine inputs. InProceedings of Supercomputing '89, pages 152–161, 1989.

  11. I. Parberry. Single-exception sorting networks and the computational complexity of optimal sorting network verification.Math. Systems Theory, 23:81–93, 1990.

    Google Scholar 

  12. D. C. Van Voorhis. An imporoved lower bound for sorting networks.IEEE Trans. Comput., 21:612–613, June 1972.

    Google Scholar 

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Author notes

  1. Ian Parberry

    Present address: Department of Computer Sciences, University of North Texas, P.O. Box 13886, 76203-3886, Denton, TX, USA

Authors and Affiliations

  1. Department of Computer Science, Penn State University, 16802, University Park, PA, USA

    Ian Parberry

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  1. Ian Parberry
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Additional information

This research was supported by NSF Grant CCR-8801659 and a Research Initiation Grant from the Pennsylvania State University.

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Parberry, I. A computer-assisted optimal depth lower bound for nine-input sorting networks. Math. Systems Theory 24, 101–116 (1991). https://doi.org/10.1007/BF02090393

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  • DOI: https://doi.org/10.1007/BF02090393

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